which graph shows a negative rate of change for the interval 0 to 2 on the x - axis?

Explanation:

Step1: Recall rate - of - change concept

The rate of change of a function $y = f(x)$ over the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$. For the interval $[0,2]$, we need to check if $f(2)-f(0)<0$. Geometrically, a negative rate of change means the function is decreasing on the interval $[0,2]$, i.e., as $x$ increases from $0$ to $2$, the $y$ - values of the function decrease.

Step2: Analyze the given graph

In the given graph, we look at the behavior of the curve from $x = 0$ to $x=2$. If the curve is going downwards (from left - to - right) in the interval $x\in[0,2]$, it has a negative rate of change.

Answer:

We need to see the full set of graphs to determine which one shows a negative rate of change on the interval $0$ to $2$ on the $x$ - axis. Since only one partial graph is provided, we cannot give a definite answer. If the graph is decreasing ( $y$ - values are getting smaller) as $x$ goes from $0$ to $2$, then that is the correct graph.